derivative of (2e^x+x^2ln(x))

Lösung

\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}

Schritte zur Lösung

\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 e^{x} + x^{2}, g = ln (x)

= \frac{d}{d x} (2 e^{x} + x^{2}) ln (x) + \frac{d}{d x} (ln (x)) (2 e^{x} + x^{2})

\frac{d}{d x} (2 e^{x} + x^{2}) = 2 e^{x} + 2 x

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= (2 e^{x} + 2 x) ln (x) + \frac{1}{x} (2 e^{x} + x^{2})

\frac{1}{x} (2 e^{x} + x^{2}) = \frac{2 e ^{x} + x ^{2}}{x}

= ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}